On 13 Jan., 00:26, Virgil <vir...@ligriv.com> wrote:> In article> <4bffb7f3-9bfa-4dae-9108-da5e24389...@f4g2000yqh.googlegroups.com>,>>>>>> WM <mueck...@rz.fh-augsburg.de> wrote:> > On 12 Jan., 22:00, Virgil <vir...@ligriv.com> wrote:> > > In article> > > <c0615860-6190-4c10-9185-78ed2f6a2...@x10g2000yqx.googlegroups.com>,>> > > WM <mueck...@rz.fh-augsburg.de> wrote:> > > > Matheology 190>> > > > The Binary Tree can be constructed by aleph_0 finite paths.>> > > > 0> > > > 1, 2> > > > 3, 4, 5, 6> > > > 7, ...>> > > Finite trees can be built having finitely many finite paths.> > > A Complete Infinite Binary Tree cannot be built with only finite paths,> > > as none of its paths can be finite.>> > Then the complete infinite set |N cannot be built with only finite> > initial segments {1, 2, 3, ..., n} and not with ony finite numbers 1,> > 2, 3, ...? Like Zuhair you are claiming infinite naturals!>> A finite initial segment of |N is not a path in the unary tree |N.>> And neither |N as a unary tree nor any Complete Infinite Binary Tree> has any finite paths.>> "A Complete Infinite Binary Tree cannot be built with only> finite paths, as none of its paths can be finite.">> Means the same as>> "A Complete Infinite Binary Tree cannot be built HAVING only> finite paths, as none of its paths can be finite.">> WM has this CRAZY notion that a path in a COMPLETE INFINITE BINARY TREE> can refer to certain finite sets of nodes.>> And no one is claiming any infinite naturals, only infinitely many> finite naturals.

So each n belongs to a finite initial segment (1,2,3,...,n).Same is valid for the nodes of the Binary Tree: Each node belongs to afinite initial segment of a path, the natural numbers (1,2,3,...,n)denoting the levels which the nodes belong to.

Everything in this model is countable. All finite initial segmentsbelong to a countable set. Everything that possibly differs from anentry of a Cantor-list belongs to a finite initial segments of theanti-diagonal. There is nothing infinite that could explain or justifyuncountability.